Abstract:
Three-dimensional Topologically Massive Gravity at its critical point has been
conjectured to be holographically dual to a Logarithmic CFT. However, many details of
this correspondence are still lacking. In this work, we study the 1-loop partition function
of Critical Cosmological Topologically Massive Gravity, previously derived by Gaberdiel,
Grumiller and Vassilevich, and show that it can be usefully rewritten as a Bell polynomial
expansion. We also show that there is a relationship between this Bell polynomial expansion
and the plethystic exponential. Our reformulation allows us to match the TMG partition
function to states on the CFT side, including the multi-particle states of t (the logarithmic
partner of the CFT stress tensor) which had previously been elusive. We also discuss the
appearance of a ladder action between the di erent multi-particle sectors in the partition
function, which induces an interesting sl(2) structure on the n-particle components of the
partition function.
